Batch Scaling Calculator
Lab to production batch scaling with mixing parameters.
About this calculator
This calculator translates a bench-scale cosmetic batch into production parameters using separate scaling laws for weight, mixing, and heating. Scale Factor is the simple ratio of production batch grams to lab batch grams (line 26). Production RPM follows the constant tip-speed rule: lab RPM multiplied by lab impeller diameter divided by production impeller diameter, so the impeller edge travels at the same meters per second at both scales (line 30). Production Mix Time scales with the diameter ratio raised to the 0.67 power, an empirical correction for larger vessels (lines 33-34).
Production Heat Time scales with the weight ratio raised to the two-thirds power, approximating volume-driven heat transfer (line 38). Lab and Production Tip Speed are computed independently from diameter and RPM for verification (lines 41-42). Power Draw Ratio combines the RPM ratio cubed with the diameter ratio to the fifth power, reflecting turbulent mixing power scaling (lines 45-46). Ingredient weights scale linearly with Scale Factor, but mixer settings do not: changing only lab batch size moves Scale Factor and heat time without altering the RPM recommendation when impeller sizes stay fixed.
Inputs
Results
Scale factor (×)
250
Production RPM
106.7
How to Use This Calculator
- Enter the lab (bench-scale) batch size in grams and the target production batch size in grams.
- Enter the lab and production mixer impeller diameters, along with the lab mixing speed, mixing time, and heating time.
- Review the scale factor and production batch weight in kilograms.
- Check the recommended production RPM, which is calculated to hold impeller tip speed constant between lab and production scale.
- Use the estimated production mixing time and heating time, along with the tip speed and power draw ratio, to plan the production run.
How the result changes with Lab batch size (g)
| Lab batch size (g) | Scale factor (×) | Production RPM |
|---|---|---|
| 100 | 500 | 106.7 |
| 150 | 333.33 | 106.7 |
| 300 | 166.67 | 106.7 |
| 500 | 100 | 106.7 |
What each input means
- Lab batch size (g)
- Weight of the lab/bench-scale batch in grams.
- Production batch (g)
- Target production batch weight in grams.
- Lab mixer diameter (cm)
- Diameter of lab mixer impeller in centimeters.
- Production mixer diameter (cm)
- Diameter of production mixer impeller in centimeters.
- Lab mixing speed (RPM)
- Lab mixer speed in revolutions per minute.
- Lab mixing time (min)
- Total mixing time at lab scale in minutes.
- Lab heat time (min)
- Time to heat oil/water phases at lab scale in minutes.
What each result means
- Scale factor (×)
- Multiplier from lab to production batch.
- Production batch (kg)
- Production batch size in kilograms.
- Production RPM
- Recommended production mixer speed to maintain constant tip speed.
- Production mix time (min)
- Estimated production mixing time based on diameter scaling.
- Production heat time (min)
- Estimated production heating time based on volume scaling.
- Lab tip speed (m/s)
- Impeller tip speed at lab scale.
- Production tip speed (m/s)
- Impeller tip speed at production scale (should match lab).
- Power draw ratio (×)
- Relative power requirement at production vs lab scale.
How this is calculated
Worked example, using the default values
- Identify Input Parameters4 parametersLab batch size (g) = 200, Production batch (g) = 50000, Lab mixer diameter (cm) = 4, Production mixer diameter (cm) = 30 = 7 input(s) provided
- Calculate Scale factorScale factor = prodBatchG / labBatchG250 = 250
- Calculate Production RPMProduction RPM = labMixSpeedRpm * (labMixerDiamCm / prodMixerDiamCm)106.7 = 106.7
- Calculate Production batchProduction batch = round((prodBatchG / 1000) * 100) / 10050 = 50
- Calculate Production mix timeProduction mix time = labMixTimeMin * pow(diamRatio, 0.67)57.9 = 57.9
Engine last updated . Checked against 3 independently-derived tests — how we verify calculators. Built by Paul Gunder, a software engineer, not a licensed financial, medical, or legal professional.
Frequently Asked Questions
Why does Production RPM drop when the production impeller is larger than the lab impeller?
The engine holds impeller tip speed constant between scales. Tip speed equals pi times diameter times RPM divided by sixty, so when production diameter grows, RPM must fall by the ratio of lab diameter to production diameter (line 30). That is why a 30 cm production impeller needs far fewer revolutions per minute than a 4 cm lab impeller at the same tip speed.
Does Scale Factor alone determine how long production mixing will take?
No. Production Mix Time depends on the diameter ratio between production and lab impellers raised to the 0.67 power, multiplied by lab mix time (lines 33-34). Scale Factor from batch weight drives Production Heat Time through the two-thirds volume exponent (line 38) but does not enter the mixing-time formula directly.
What does Power Draw Ratio tell me about equipment sizing?
Power Draw Ratio estimates how much more motor power production needs relative to lab, using the production-to-lab RPM ratio cubed times the production-to-lab diameter ratio to the fifth power (lines 45-46). It rises sharply with impeller size even when tip speed is matched, helping you check whether the production mixer can deliver enough torque.
Will Lab Tip Speed and Production Tip Speed always match in the results?
They should match closely because Production RPM is derived specifically to preserve lab tip speed when impeller diameters differ (lines 30, 41-42). Both values are reported separately so you can confirm the scale-up math before committing to a production run schedule.
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